Dynamic Stresses in 3D Elastic Solids with Pairwise Disk-Shaped Gaps within One-Periodic Lattice

The symmetric problem of harmonic in time elastic wave scattering by a periodic array of pairwise arranged coplanar disk-shaped gaps embedded in an boundless three-dimensional solid is solved via numerical computation. The identical gap pairs are positioned along a single periodic direction with equal distances between adjacent pairs, introducing a one-periodic discontinuity pattern into the solid. By exploiting the superposition principle and enforcing the boundary conditions on the multiply connected domain, in conjunction with the natural symmetry conditions resulting from the periodic arrangement, the problem is reduced to the system of two boundary integral equations (BIEs). The mode-I dynamic stress intensity factor (SIF) in the gap vicinities depending on the angular coordinate and frequency is calculated and analyzed.